Osaka Journal of Mathematics

On the splitting principle of bundle gerbe modules

Atsushi Tomoda

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Abstract

We introduce the notion of an $n$-trivialization and a compatible curving and construct the splitting of bundle gerbe modules to define the twisted Chern classes and the twisted Chern character for bundle gerbe modules in terms of algebraic topology. Moreover, we prove that the latter coincides with the twisted Chern character due to Bouwknegt-Carey-Mathai-Murray-Stevenson [1] if the bundle gerbe is given an $n$-trivialization and a compatible curving.

Article information

Source
Osaka J. Math., Volume 44, Number 1 (2007), 231-246.

Dates
First available in Project Euclid: 19 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1174324334

Mathematical Reviews number (MathSciNet)
MR2313038

Zentralblatt MATH identifier
1133.19002

Subjects
Primary: 55R65: Generalizations of fiber spaces and bundles
Secondary: 55R20: Spectral sequences and homology of fiber spaces [See also 55Txx]

Citation

Tomoda, Atsushi. On the splitting principle of bundle gerbe modules. Osaka J. Math. 44 (2007), no. 1, 231--246. https://projecteuclid.org/euclid.ojm/1174324334


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References

  • P. Bouwknegt, A. Carey, V. Mathai, M.K. Murray, and D. Stevenson: Twisted $K$-theory and $K$-theory of bundle gerbes, Comm. Math. Phys. 228 (2002), 17--45.
    Mathematical Reviews (MathSciNet): MR1911247
    Digital Object Identifier: doi:10.1007/s002200200646
    Zentralblatt MATH: 1036.19005
  • M.K. Murray: Bundle gerbes, J. London. Math. Soc. (2) 54 (1996), 403--416.
    Mathematical Reviews (MathSciNet): MR1405064
  • M.K. Murray and D. Stevenson: Bundle gerbes: stable isomorphism and local theory, J. London. Math. Soc. (2) 62 (2000), 925--937.
    Mathematical Reviews (MathSciNet): MR1794295
    Digital Object Identifier: doi:10.1112/S0024610700001551
    Zentralblatt MATH: 1019.55009
  • D. Husemoller: Fibre Bundles, second edition, Graduate Texts in Math. 20, Springer-Verlag, New York, 1975.
    Mathematical Reviews (MathSciNet): MR370578
    Zentralblatt MATH: 0307.55015

Osaka University and Osaka City University, Departments of Mathematics

Osaka Journal of Mathematics

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